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dc.contributor.advisor Sorensen, Danny C.
dc.creatorChaturantabut, Saifon
dc.date.accessioned 2011-07-25T01:39:32Z
dc.date.available 2011-07-25T01:39:32Z
dc.date.issued 2009
dc.identifier.urihttps://hdl.handle.net/1911/61925
dc.description.abstract This thesis evaluates and compares the efficiencies of techniques for constructing reduced-order models for finite difference (FD) and finite element (FE) discretized systems of unsteady nonlinear partial differential equations (PDEs). With nonlinearity, the complexity for solving the reduced-order system constructed directly from the well-known Proper Orthogonal Decomposition (POD) technique alone still depends on the dimension of the original system. Empirical Interpolation Method (EIM), proposed in [2], and its discrete variation, Discrete Empirical Interpolation Method (DEIM), introduced in this thesis, are therefore combined with the POD technique to remove this inefficiency in the nonlinear terms of FE and FD cases, respectively. Numerical examples demonstrate that both POD-EIM and POD-DEIM approaches not only dramatically reduce the dimension of the original system with high accuracy, but also remove the dependence on the dimension of the original system as reflected in the decrease computational time compared to the POD approach.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
Computer science
dc.title Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Chemistry
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Masters
thesis.degree.name Master of Arts
dc.identifier.citation Chaturantabut, Saifon. "Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods." (2009) Master’s Thesis, Rice University. https://hdl.handle.net/1911/61925.


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